Lorentz factor for particle moving at angle

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SUMMARY

The discussion centers on the Lorentz factor in the context of relativistic velocities, specifically addressing the transformation of angles for a particle moving at an angle. The formula presented, tanθ' = u'y / u'x, raises questions about the application of the Lorentz factor (γ) to the denominator of u'y but not to u'x. This approach is based on established relativistic velocity addition principles. Understanding the derivation of these formulas is crucial for grasping the underlying physics.

PREREQUISITES
  • Understanding of Lorentz transformations
  • Familiarity with the Lorentz factor (γ)
  • Basic knowledge of trigonometric functions in physics
  • Concept of relativistic velocity addition
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  • Study the derivation of Lorentz transformations in detail
  • Learn about the implications of the Lorentz factor (γ) in different contexts
  • Explore relativistic velocity addition and its applications
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Physicists, students of relativity, and anyone interested in understanding the behavior of particles at relativistic speeds.

ZedCar
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It's not a homework question, but I noticed on this webpage;

http://www.relativitycalculator.com/addition_relativistic_velocities.shtml

near the very bottom there is a section entitled, "What, therefore, would r & θ appear to be to an observor in relatively moving S'?"

Example 1

the formula then states:

tanθ' = u'y / u'x I understand why they're doing this. Though after this, can anyone explain the next part of the progression? Why have they applied a γ to the denominator of u'y but not to u'x ?

Thank you
 
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They're just applying the formulas derived in the previous section. Do you understand the derivation?
 

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